BEHAVIOR OF LINEAR RECONSTRUCTION TECHNIQUES ON UNSTRUCTURED MESHES

This paper presents an assessment of a variety of reconstruction schem es on meshes with both quadrilateral and triangular tessellations, The investigations measure the order of accuracy, absolute error, and con vergence properties associated with each method. Linear reconstruction approaches using both Green-Gauss and least-squares gradient estimati on are evaluated against a structured MUSCL scheme wherever possible, In addition to examining the influence of polygon degree and reconstru ction strategy, results with three limiters are examined and compared against unlimited results when feasible. The methods are applied on qu adrilateral, right triangular, and equilateral triangular elements to facilitate an examination of the scheme's behavior on a variety of ele ment shapes. The numerical test cases include feell-noown internal and external inviscid examples and also a supersonic vortex problem for w hich there exists a closed-form solution to the two-dimensional compre ssible Euler equations. Such investigations indicate that the least-sq uares gradient estimation provides significantly more reliable results on poor quality meshes. Furthermore, limiting only the face normal co mponent of the gradient can significantly increase both accuracy and c onvergence while still preserving the integral cell average and mainta ining monoticity. The first-order method performs poorly on stretched triangular meshes, and analysis shows that such meshes result in poorl y aligned left and right states for the Riemann problem. The higher av erage valence of a vertex in the triangular tesselations does not appe ar to enhance the wave propagation, accuracy, or convergence propertie s of the method. Typically, quadrilateral elements provide superior or equivalent discrete solutions with approximately 50% fewer edges in t he domain two-dimensional. However, on very poor quality meshes, the t riangular elements routinely yield superior accuracy as a result of th e trapezoidal quadrature of the Galerkin portion of the numerical flux function.